The resulting restraints, forces and trajectories were analysed using a locally
developed python script, where the MDAnalysis library
[1]}, [2]}
was used for calculating the O-H distances.
The errors reported here were calculated by the method outlined by Flyvbjerg
and Petersen.[3]}
The errors of the cut off distance \(R_c\)  and the probabilistic p\(K_A\)  or p\(K_W\)  are
not considered to be correlated, i.e., the errors in p\(K_W\)  or p\(K_A\)  are
calculated using a fixed value of \(R_c\) .
All figures depicting the molecular systems were visualized using the VMD
software.[4]}
The numerical integrals needed for the calculations outlined in the theory section
were all carried out using linear interpolation and a step size of \(1\cdot 10^{-4}\) 
in both CN and O-H distance space.
